The Pythagorean Theorem Objective: Find the length of a using the Pythagorean Theorem.

Interesting fact: “The name of Pythagoras was selected for this theorem not because he discovered it - - the Pythagorean theorem or Pythagorean triples had been in use for centuries. -- but perhaps because Pythagoras was the first to prove the theorem.” He also did many cool inventions such as the Pythagoras Cup…

We use the Pythagorean Theorem when we want to know the remaining length of the side of a right triangle for which we already know two lengths. In a right triangle the 2 sides that form the right triangle are called legs. The side opposite the right angle is called the hypotenuse. It is the longest side of the triangle. The Pythagorean Theorem describes the relationship between the length of the hypotenuse and the length of the legs.

The Pythagorean Theorem states: In a Right Triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. a2 + b2 = c2

Example: Find the missing length in each right triangle. Steps to find the hypotenuse: Use the Pythagorean theorem. Replace a and b with their respective numbers: a with 3 and b with 4. Square 3 and 4. Add Find the square root. a2 + b2 = c2 32 + 42 = C2 9 + 16 = C2 25 = c2 5 = C

Example 2: Find the missing length in each right triangle. Steps: Use Pythagorean Theorem. Replace b with 6 and c with 10. Square 6 and 10. We “undo” the addition. We do this by subtracting 36 from each side. Solve. Find the square root. a2 + b2 = c2 a2 + 62 = 102 a2 + 36 = 100 - 36 - 36 a2 = 64 a = 8

Homework: Find the missing angle in the right triangle. 1. 4. 2. 5. 3. 6.